2. 2
2
Data Preprocessing
Data Preprocessing: An Overview
Why Preprocess the Data ?
Forms of Data Preprocessing
Data Cleaning
Data Integration and Transformation
Data Reduction
Data Transformation and Data Discretization
Summary
3. 3
Why Preprocess the Data?
Accuracy: correct or wrong, accurate or not
Completeness: not recorded, unavailable, …
Consistency: some modified but some not, dangling, …
Timeliness: timely update?
Believability: how trustable the data are correct?
Interpretability: how easily the data can be
understood?
4. 4
Forms of Data Preprocessing
Data cleaning
Fill in missing values, smooth noisy data, identify or remove
outliers, and resolve inconsistencies
Data integration
Integration of multiple databases, data cubes, or files
Data reduction
Dimensionality reduction
Numerosity reduction
Data compression
Data transformation and data discretization
Normalization
Concept hierarchy generation
5. 5
Data Cleaning
Data in the Real World Is Dirty: Lots of potentially incorrect data,
e.g., instrument faulty, human or computer error, transmission error
incomplete: lacking attribute values, lacking certain attributes of
interest, or containing only aggregate data
e.g., Occupation=“ ” (missing data)
noisy: containing noise, errors, or outliers
e.g., Salary=“−10” (an error)
inconsistent: containing discrepancies in codes or names, e.g.,
Age=“42”, Birthday=“03/07/2010”
Was rating “1, 2, 3”, now rating “A, B, C”
discrepancy between duplicate records
Intentional (e.g., disguised missing data)
Jan. 1 as everyone’s birthday?
6. 6
Incomplete (Missing) Data
Data is not always available
E.g., many tuples have no recorded value for several
attributes, such as customer income in sales data
Missing data may be due to
equipment malfunction
inconsistent with other recorded data and thus deleted
data not entered due to misunderstanding
certain data may not be considered important at the
time of entry
not register history or changes of the data
Missing data may need to be inferred
7. 7
How to Handle Missing Data?
Ignore the tuple: usually done when class label is missing
(when doing classification)—not effective when the % of
missing values per attribute varies considerably
Fill in the missing value manually: tedious + infeasible?
Fill in it automatically with
a global constant : e.g., “unknown”, a new class?!
the attribute mean
the attribute mean for all samples belonging to the
same class: smarter
the most probable value: inference-based such as
Bayesian formula or decision tree
8. 8
Noisy Data
Noise: random error or variance in a measured variable
Incorrect attribute values may be due to
faulty data collection instruments
data entry problems
data transmission problems
technology limitation
inconsistency in naming convention
Other data problems which require data cleaning
duplicate records
incomplete data
inconsistent data
9. 9
How to Handle Noisy Data?
Binning
first sort data and partition into (equal-frequency) bins
then one can smooth by bin means, smooth by bin
median, smooth by bin boundaries, etc.
Regression
smooth by fitting the data into regression functions
Clustering
detect and remove outliers
Combined computer and human inspection
detect suspicious values and check by human (e.g.,
deal with possible outliers)
10. 10
Data Cleaning as a Process
Data discrepancy detection
Use metadata (e.g., domain, range, dependency, distribution)
Check field overloading
Check uniqueness rule, consecutive rule and null rule
Use commercial tools
Data scrubbing: use simple domain knowledge (e.g., postal
code, spell-check) to detect errors and make corrections
Data auditing: by analyzing data to discover rules and
relationship to detect violators (e.g., correlation and clustering
to find outliers)
Data migration and integration
Data migration tools: allow transformations to be specified
ETL (Extraction/Transformation/Loading) tools: allow users to
specify transformations through a graphical user interface
Integration of the two processes
Iterative and interactive (e.g., Potter’s Wheels)
11. 11
11
Data Integration
Data integration:
Combines data from multiple sources into a coherent store
Schema integration: e.g., A.cust-id B.cust-#
Integrate metadata from different sources
Entity identification problem:
Identify real world entities from multiple data sources, e.g., Bill
Clinton = William Clinton
Detecting and resolving data value conflicts
For the same real world entity, attribute values from different
sources are different
Possible reasons: different representations, different scales, e.g.,
metric vs. British units
12. 12
12
Handling Redundancy in Data
Integration
Redundant data occur often when integration of multiple
databases
Object identification: The same attribute or object
may have different names in different databases
Derivable data: One attribute may be a “derived”
attribute in another table, e.g., annual revenue
Redundant attributes may be able to be detected by
correlation analysis and covariance analysis
Careful integration of the data from multiple sources may
help reduce/avoid redundancies and inconsistencies and
improve mining speed and quality
13. 13
Correlation Analysis (Nominal Data)
Χ2 (chi-square) test
The larger the Χ2 value, the more likely the variables are
related
The cells that contribute the most to the Χ2 value are
those whose actual count is very different from the
expected count
Correlation does not imply causality
# of hospitals and # of car-theft in a city are correlated
Both are causally linked to the third variable: population
Expected
Expected
Observed 2
2 )
(
14. 14
Correlation Analysis (Numeric Data)
Correlation coefficient (also called Pearson’s product
moment coefficient)
where n is the number of tuples, and are the respective
means of A and B, σA and σB are the respective standard deviation
of A and B, and Σ(aibi) is the sum of the AB cross-product.
If rA,B > 0, A and B are positively correlated (A’s values
increase as B’s). The higher, the stronger correlation.
rA,B = 0: independent; rAB < 0: negatively correlated
B
A
n
i i
i
B
A
n
i i
i
B
A
n
B
A
n
b
a
n
B
b
A
a
r
)
1
(
)
(
)
1
(
)
)(
( 1
1
,
A B
16. 16
Covariance (Numeric Data)
Covariance is similar to correlation
where n is the number of tuples, and are the respective mean or
expected values of A and B, σA and σB are the respective standard
deviation of A and B.
Positive covariance: If CovA,B > 0, then A and B both tend to be larger
than their expected values.
Negative covariance: If CovA,B < 0 then if A is larger than its expected
value, B is likely to be smaller than its expected value.
Independence: CovA,B = 0 but the converse is not true:
Some pairs of random variables may have a covariance of 0 but are not
independent. Only under some additional assumptions (e.g., the data follow
multivariate normal distributions) does a covariance of 0 imply independence
A B
Correlation coefficient:
17. 17
Data Reduction Strategies
Data reduction: Obtain a reduced representation of the data set that
is much smaller in volume but yet produces the same (or almost the
same) analytical results
Why data reduction? — A database/data warehouse may store
terabytes of data. Complex data analysis may take a very long time to
run on the complete data set.
Data reduction strategies
Dimensionality reduction, e.g., remove unimportant attributes
Wavelet transforms
Principal Components Analysis (PCA)
Feature subset selection, feature creation
Numerosity reduction (some simply call it: Data Reduction)
Regression and Log-Linear Models
Histograms, clustering, sampling
Data cube aggregation
Data compression
18. 18
Data Reduction 1: Dimensionality
Reduction
Curse of dimensionality
When dimensionality increases, data becomes increasingly sparse
Density and distance between points, which is critical to clustering, outlier
analysis, becomes less meaningful
The possible combinations of subspaces will grow exponentially
Dimensionality reduction
Avoid the curse of dimensionality
Help eliminate irrelevant features and reduce noise
Reduce time and space required in data mining
Allow easier visualization
Dimensionality reduction techniques
Wavelet transforms
Principal Component Analysis
Supervised and nonlinear techniques (e.g., feature selection)
19. 19
Mapping Data to a New Space
Two Sine Waves Two Sine Waves + Noise Frequency
Fourier transform
Wavelet transform
20. 20
x2
x1
e
Principal Component Analysis (PCA)
Find a projection that captures the largest amount of variation in data
The original data are projected onto a much smaller space, resulting
in dimensionality reduction. We find the eigenvectors of the
covariance matrix, and these eigenvectors define the new space
21. 21
Given N data vectors from n-dimensions, find k ≤ n orthogonal vectors
(principal components) that can be best used to represent data
Normalize input data: Each attribute falls within the same range
Compute k orthonormal (unit) vectors, i.e., principal components
Each input data (vector) is a linear combination of the k principal
component vectors
The principal components are sorted in order of decreasing
“significance” or strength
Since the components are sorted, the size of the data can be
reduced by eliminating the weak components, i.e., those with low
variance (i.e., using the strongest principal components, it is
possible to reconstruct a good approximation of the original data)
Works for numeric data only
Principal Component Analysis
(Steps)
22. 22
Attribute Subset Selection
Another way to reduce dimensionality of data
Redundant attributes
Duplicate much or all of the information contained in
one or more other attributes
E.g., purchase price of a product and the amount of
sales tax paid
Irrelevant attributes
Contain no information that is useful for the data
mining task at hand
E.g., students' ID is often irrelevant to the task of
predicting students' GPA
23. 23
Attribute Creation (Feature
Generation)
Create new attributes (features) that can capture the
important information in a data set more effectively than
the original ones
Three general methodologies
Attribute extraction
Domain-specific
Mapping data to new space (see: data reduction)
E.g., Fourier transformation, wavelet
transformation, manifold approaches (not covered)
Attribute construction
Combining features (see: discriminative frequent
patterns in Chapter 7)
Data discretization
24. 24
Data Reduction 2: Numerosity
Reduction
Reduce data volume by choosing alternative, smaller
forms of data representation
Parametric methods (e.g., regression)
Assume the data fits some model, estimate model
parameters, store only the parameters, and discard
the data (except possible outliers)
Ex.: Log-linear models—obtain value at a point in m-
D space as the product on appropriate marginal
subspaces
Non-parametric methods
Do not assume models
Major families: histograms, clustering, sampling, …
25. 25
Parametric Data Reduction:
Regression and Log-Linear Models
Linear regression
Data modeled to fit a straight line
Often uses the least-square method to fit the line
Multiple regression
Allows a response variable Y to be modeled as a
linear function of multidimensional feature vector
Log-linear model
Approximates discrete multidimensional probability
distributions
26. 26
Regression Analysis
Regression analysis: A collective name for
techniques for the modeling and analysis
of numerical data consisting of values of a
dependent variable (also called
response variable or measurement) and
of one or more independent variables (aka.
explanatory variables or predictors)
The parameters are estimated so as to give
a "best fit" of the data
Most commonly the best fit is evaluated by
using the least squares method, but
other criteria have also been used
Used for prediction
(including forecasting of
time-series data), inference,
hypothesis testing, and
modeling of causal
relationships
y
x
y = x + 1
X1
Y1
Y1’
27. 27
Linear regression: Y = w X + b
Two regression coefficients, w and b, specify the line and are to be
estimated by using the data at hand
Using the least squares criterion to the known values of Y1, Y2, …,
X1, X2, ….
Multiple regression: Y = b0 + b1 X1 + b2 X2
Many nonlinear functions can be transformed into the above
Log-linear models:
Approximate discrete multidimensional probability distributions
Estimate the probability of each point (tuple) in a multi-dimensional
space for a set of discretized attributes, based on a smaller subset
of dimensional combinations
Useful for dimensionality reduction and data smoothing
Regress Analysis and Log-Linear
Models
28. 28
Histogram Analysis
Divide data into buckets and
store average (sum) for each
bucket
Partitioning rules:
Equal-width: equal bucket
range
Equal-frequency (or equal-
depth)
0
5
10
15
20
25
30
35
40
10000
20000
30000
40000
50000
60000
70000
80000
90000
100000
29. 29
Clustering
Partition data set into clusters based on similarity, and
store cluster representation (e.g., centroid and diameter)
only
Can be very effective if data is clustered but not if data
is “smeared”
Can have hierarchical clustering and be stored in multi-
dimensional index tree structures
There are many choices of clustering definitions and
clustering algorithms
Cluster analysis will be studied in depth in Chapter 10
30. 30
Sampling
Sampling: obtaining a small sample s to represent the
whole data set N
Allow a mining algorithm to run in complexity that is
potentially sub-linear to the size of the data
Key principle: Choose a representative subset of the data
Simple random sampling may have very poor
performance in the presence of skew
Develop adaptive sampling methods, e.g., stratified
sampling:
Note: Sampling may not reduce database I/Os (page at a
time)
31. 31
Data Cube Aggregation
The lowest level of a data cube (base cuboid)
The aggregated data for an individual entity of interest
E.g., a customer in a phone calling data warehouse
Multiple levels of aggregation in data cubes
Further reduce the size of data to deal with
Reference appropriate levels
Use the smallest representation which is enough to
solve the task
Queries regarding aggregated information should be
answered using data cube, when possible
32. 32
Data Reduction 3: Data
Compression
String compression
There are extensive theories and well-tuned algorithms
Typically lossless, but only limited manipulation is
possible without expansion
Audio/video compression
Typically lossy compression, with progressive refinement
Sometimes small fragments of signal can be
reconstructed without reconstructing the whole
Time sequence is not audio
Typically short and vary slowly with time
Dimensionality and numerosity reduction may also be
considered as forms of data compression
34. 34
Data Transformation
A function that maps the entire set of values of a given attribute to a
new set of replacement values s.t. each old value can be identified
with one of the new values
Methods
Smoothing: Remove noise from data
Attribute/feature construction
New attributes constructed from the given ones
Aggregation: Summarization, data cube construction
Normalization: Scaled to fall within a smaller, specified range
min-max normalization
z-score normalization
normalization by decimal scaling
Discretization: Concept hierarchy climbing
35. 35
Normalization
Min-max normalization: to [new_minA, new_maxA]
Ex. Let income range $12,000 to $98,000 normalized to [0.0,
1.0]. Then $73,000 is mapped to
Z-score normalization (μ: mean, σ: standard deviation):
Ex. Let μ = 54,000, σ = 16,000. Then
Normalization by decimal scaling
716
.
0
0
)
0
0
.
1
(
000
,
12
000
,
98
000
,
12
600
,
73
A
A
A
A
A
A
min
new
min
new
max
new
min
max
min
v
v _
)
_
_
(
'
A
A
v
v
'
j
v
v
10
' Where j is the smallest integer such that Max(|ν’|) < 1
225
.
1
000
,
16
000
,
54
600
,
73
36. 36
Discretization
Three types of attributes
Nominal—values from an unordered set, e.g., color, profession
Ordinal—values from an ordered set, e.g., military or academic
rank
Numeric—real numbers, e.g., integer or real numbers
Discretization: Divide the range of a continuous attribute into intervals
Interval labels can then be used to replace actual data values
Reduce data size by discretization
Supervised vs. unsupervised
Split (top-down) vs. merge (bottom-up)
Discretization can be performed recursively on an attribute
Prepare for further analysis, e.g., classification
37. 37
Data Discretization Methods
Typical methods: All the methods can be applied recursively
Binning
Top-down split, unsupervised
Histogram analysis
Top-down split, unsupervised
Clustering analysis (unsupervised, top-down split or
bottom-up merge)
Decision-tree analysis (supervised, top-down split)
Correlation (e.g., 2) analysis (unsupervised, bottom-up
merge)
38. 38
Simple Discretization: Binning
Equal-width (distance) partitioning
Divides the range into N intervals of equal size: uniform grid
if A and B are the lowest and highest values of the attribute, the
width of intervals will be: W = (B –A)/N.
The most straightforward, but outliers may dominate presentation
Skewed data is not handled well
Equal-depth (frequency) partitioning
Divides the range into N intervals, each containing approximately
same number of samples
Good data scaling
Managing categorical attributes can be tricky
39. 39
Binning Methods for Data
Smoothing
Sorted data for price (in dollars): 4, 8, 9, 15, 21, 21, 24, 25, 26,
28, 29, 34
* Partition into equal-frequency (equi-depth) bins:
- Bin 1: 4, 8, 9, 15
- Bin 2: 21, 21, 24, 25
- Bin 3: 26, 28, 29, 34
* Smoothing by bin means:
- Bin 1: 9, 9, 9, 9
- Bin 2: 23, 23, 23, 23
- Bin 3: 29, 29, 29, 29
* Smoothing by bin boundaries:
- Bin 1: 4, 4, 4, 15
- Bin 2: 21, 21, 25, 25
- Bin 3: 26, 26, 26, 34
41. 41
Discretization by Classification
& Correlation Analysis
Classification (e.g., decision tree analysis)
Supervised: Given class labels, e.g., cancerous vs. benign
Using entropy to determine split point (discretization point)
Top-down, recursive split
Details to be covered in Chapter 7
Correlation analysis (e.g., Chi-merge: χ2-based discretization)
Supervised: use class information
Bottom-up merge: find the best neighboring intervals (those
having similar distributions of classes, i.e., low χ2 values) to merge
Merge performed recursively, until a predefined stopping condition
42. 42
Concept Hierarchy Generation
Concept hierarchy organizes concepts (i.e., attribute values)
hierarchically and is usually associated with each dimension in a data
warehouse
Concept hierarchies facilitate drilling and rolling in data warehouses to
view data in multiple granularity
Concept hierarchy formation: Recursively reduce the data by collecting
and replacing low level concepts (such as numeric values for age) by
higher level concepts (such as youth, adult, or senior)
Concept hierarchies can be explicitly specified by domain experts
and/or data warehouse designers
Concept hierarchy can be automatically formed for both numeric and
nominal data. For numeric data, use discretization methods shown.
43. 43
Concept Hierarchy Generation
for Nominal Data
Specification of a partial/total ordering of attributes
explicitly at the schema level by users or experts
street < city < state < country
Specification of a hierarchy for a set of values by explicit
data grouping
{Urbana, Champaign, Chicago} < Illinois
Specification of only a partial set of attributes
E.g., only street < city, not others
Automatic generation of hierarchies (or attribute levels) by
the analysis of the number of distinct values
E.g., for a set of attributes: {street, city, state, country}
44. 44
Automatic Concept Hierarchy
Generation
Some hierarchies can be automatically generated based on
the analysis of the number of distinct values per attribute in
the data set
The attribute with the most distinct values is placed at
the lowest level of the hierarchy
Exceptions, e.g., weekday, month, quarter, year
country
province_or_ state
city
street
15 distinct values
365 distinct values
3567 distinct values
674,339 distinct values
45. 45
Summary
Data quality: accuracy, completeness, consistency, timeliness,
believability, interpretability
Data cleaning: e.g. missing/noisy values, outliers
Data integration from multiple sources:
Entity identification problem
Remove redundancies
Detect inconsistencies
Data reduction
Dimensionality reduction
Numerosity reduction
Data compression
Data transformation and data discretization
Normalization
Concept hierarchy generation
